The nuclear accident at Three Mile Island in Spring 1979 produced more
than radioactive fall-out. There was also publication of a Rasch
analysis in a statistical journal. "[There is] a method for obtaining
CMLE's [conditional maximum likelihood estimates] in the Rasch model
with standard log-linear model programs such as GLIM and SPSS-X ...
[This] method is used to analyze the data from the Three Mile Island
study" (Conaway, 1989). What message does this paper have for Rasch
measurement practitioners?

Stress in 267 mothers of young children living within 10 miles of the
plant were surveyed over three years. 115 mothers, living within 5
miles of the reactor, were assigned to group LT5. The other 152
mothers, living 6 or more miles away, were assigned to group GT5.
Each mother was interviewed four times, and her stress level rated
high, medium or low. The data were originally published by Fienberg
et al. (1985).

Conaway implemented a Rasch model in his logit-linear regression.
From Table 1, one of his simpler tables, he concludes that "for the
LT5 group, ... levels of stress did not change [significantly] over
time". From other tables, he concludes that "in the GT5 group ...
there are significant decreases in the levels of stress" (p.58). Even
after reading both Conaway and Fienberg, however, I was unclear as to
what had happened to mothers' stress levels. Fortunately the data
matrix was also published. This afforded the opportunity to reanalyze
the data with standard Rasch analysis software.

One approach is a fixed-effects, one-facet Rasch analysis (implemented with Facets). At each of
time-point, each group of mothers can be thought of as random
replications of a shared group/time-point stress. Since 2 groups are
rated at 4 time-points, there are 8 time-point effects. Each stress
rating is classified solely by group/time-point, ignoring information
about which mother is rated. Thus there is just one facet containing
8 group/time-point elements. Each of the four LT5 time-point elements
has 115 observations. Each of the four GT5 time-point elements has
152 observations. Since the survey is intended to have a uniform
rating scale, only one rating scale structure is modelled. (An
equivalent BIGSTEPS result is obtained by using a data matrix of 257
mothers by 8 group/time-points and anchoring all mothers at zero
logits. Then the time-point and rating scale calibrations can be used
as anchors for the analysis of time-serial effects.) The Facets
output is shown in Table 2. A zero logit measure corresponds to
medium stress.

The rating scale step calibrations placed the low stress region at
-1.44 logits and below, and the high stress region at 1.44 logits and
above. The mean-square variance ratio, "Mnsq", quantifies the extent
of central tendency in the stress ratings. Values above 1.0 indicate
unexpected heterogeneity in the stress ratings across mothers. Values
less than 1.0 indicate unexpected homogeneity. We see that the
ratings of the GT5 group are more homogeneous than those of the LT5
group.

Most interesting is how stress changed over time. A plot of the 8
time-point calibrations is shown in the Figure. Immediately after the
accident, the two groups of mothers were equally stressed. As time
passed, the more distant GT5 group relaxed more than the LT5 group.
Since each plotted point has a standard error of about 0.15 logits,
the only statistically remarkable points are the first and second time
points of the GT5 group. They report a significant drop in stress
between Winter 1979 and Spring 1980.

What is the message? Even one-facet analysis can be useful. Though
Conaway's analysis is intricate, meticulous and detailed, one simple
plot can capture the whole story.
John Michael Linacre

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The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.